This work aims to provide an approach to the macroscopic modeling and simulation of pedestrian flow, coupled with contagion spreading, towards numerical investigation of the effect of certain, macro-control measures on epidemics transport dynamics. To model the dynamics of the pedestrians, a second-order macroscopic model, coupled with an Eikonal equation, is used. This model is coupled with a macroscopic Susceptible-Exposed-Infected-Susceptible-Vaccinated (SEISV) contagion model, where the force-of-infection $\beta$ coefficient is modeled via a drift-diffusion equation, which is affected by the air-flow dynamics due to the ventilation. The air-flow dynamics are obtained assuming a potential flow that can imitate the existence of ventilation in the computational domain. Numerical approximations are considered for the coupled model along with numerical tests and results. In particular, we investigate the effect of employment of different, epidemics transport control measures, which may be implemented through real-time manipulation of i) ventilation rate and direction, ii) maximum speed of pedestrians, and iii) average distances between pedestrians, and through iv) incorporation in the crowd of masked or vaccinated individuals. Such simulations of disease spreading in a moving crowd can potentially provide valuable information about the risks of infection in relevant situations and support the design of systematic intervention/control measures.

翻译：本研究旨在提出一种宏观建模与模拟方法，结合行人流动与传染扩散过程，用于数值研究特定宏观控制措施对流行病传播动力学的影响。行人动力学建模采用二阶宏观模型与Eikonal方程耦合的建模框架。该模型进一步与宏观SEISV（易感-潜伏-感染-易感-接种）传染病模型耦合，其中感染率系数$\beta$通过漂移-扩散方程进行建模，该系数受通风气流动力学的影响。气流动力学通过势流假设获得，以模拟计算域中通风系统的存在。针对该耦合模型提出了数值近似方法，并进行了数值测试与结果分析。我们重点研究了不同流行病传播控制措施的实施效果，这些措施可通过以下方式的实时调控实现：i) 通风速率与方向，ii) 行人最大移动速度，iii) 行人间平均距离，以及 iv) 人群中佩戴口罩或接种疫苗个体的比例。此类移动人群中疾病传播的模拟研究，可为相关情境下的感染风险评估提供有价值的信息，并支持系统性干预/控制措施的设计。